Two-dimensional classical XY models and the effect of symmetry-breaking fields

Jae-Kwon Kim

I. Nakayama, T. Tsuneto

The effect of symmetry-breaking fields cos pθ(r) on the thermodynamic properties of a classical XY model in two dimensions is analyzed in detail. By means of the Coulomb gas representation of Kadanoff and the graphic expansion for small fugacities, we examine the effective interaction potentials Gjj(r) between charged particles and find the phase structures in the whole range of temperature and for all p. Studying Gjj(r) gives differential equations similar to the renormalization group equations of Kosterlitz and especially the singular variation of the correlation length at the phase transitions for p≥5. To see the thermodynamic properties of each phase, we also study the spin correlation function and the spontaneous magnetization.

Thomas Delica, Rainer W Gerling, Hajo Leschke

Thermal properties of the one-dimensional classical XY-model in a symmetry-breaking field are studied by using the transfer-kernel method. The results complete earlier data from Monte-Carlo simulations.

G. Dresselhaus, Kwok Yip Szeto

Tessa Cookmeyer, S. Das Sarma

We theoretically consider bilayers of two-dimensional (2D) electron gases as in semiconductor quantum wells, and investigate possible spontaneous symmetry breaking transitions at low carrier densities driven by interlayer Coulomb interactions. We use a self-consistent technique implementing mean-field truncations of the interacting four-fermion terms, and find a U(1) layer symmetry breaking transition at low carrier densities where the individual layer identities are lost leading to an effective pseudospin XY ferromagnet in the 2D plane. Our results validate earlier theoretical studies using simpler restricted Hartree-Fock techniques, and establish the pseudospin XY ferromagnet as a possible low-density symmetry broken phase of 2D bilayers.

Enrico Rastelli, Sofia Regina, A. Tassi